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VectorCalculus

  

RadiusOfCurvature

  

compute the radius of curvature of a curve

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RadiusOfCurvature(C, t)

Parameters

C

-

free or position Vector or Vector valued procedure; specify the components of the curve

t

-

(optional) name; specify the parameter of the curve

Description

• 

The RadiusOfCurvature(C, t) command computes the radius of curvature of the curve C.  This is defined to be 1/Curvature(C, t) when the curvature is not zero and infinity when the curvature is zero.

• 

The curve C can be specified as a free or positionVector or a Vector valued procedure, which determines the returned object type.

• 

If t is not specified, the function tries to determine a suitable variable name from the components of C.  To do this, it checks all of the indeterminates of type name in the components of C and removes the ones which are determined to be constants.

  

If the resulting set has a single entry, this single entry is the variable name.  If it has more than one entry, an error is raised.

• 

If a coordinate system attribute is specified on C, C is interpreted in this coordinate system.  Otherwise, the curve is interpreted as a curve in the current default coordinate system.  If the two are not compatible, an error is raised.

Examples

withVectorCalculus:

RadiusOfCurvaturecost,sint,t

1

(1)

RadiusOfCurvaturePositionVectorcost,sint,t

2

(2)

rRadiusOfCurvaturet→t,t2,t3

rt→129t4+4t2+19t4+9t2+19t4+4t2+12

(3)

RadiusOfCurvatureacost,asint,tassuminga::constant

a2+1a2a2+1

(4)

SetCoordinates'polar'

polar

(5)

RadiusOfCurvatureⅇt,t

2ⅇ2t

(6)

See Also

assuming

VectorCalculus

VectorCalculus[Binormal]

VectorCalculus[Curvature]

VectorCalculus[GetCoordinates]

VectorCalculus[PrincipalNormal]

VectorCalculus[SetCoordinates]

VectorCalculus[TangentVector]

VectorCalculus[TNBFrame]

VectorCalculus[Torsion]

VectorCalculus[Vector]